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Matrix Solution

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Jair
Jair 2011-11-21
评论： Joshua Magno 2016-10-13
The elements of the symmetric Pascal matrix are obtained from: Pij = (i + j - 2)!/(j - 1)!(j - 1)! Write a MATLAB program that creates an n by n symmetric Pascal matrix. Use the program to create a 4x4 and 7x7 Pascal matrices.
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Joshua Magno
Joshua Magno 2016-10-13
function X=matrix
n=input('Enter the number of rows: ');
m=input('Enter the number of columns: ');
A=[]; % define an empty matrix
for k=1:n
for h=1:m if k==1
A(k,h)=k;
elseif h==1
A(k,h)=h;
else
A(k,h)=A(k,h-1) + A(k-1,h); %assign values to other elements
end
end
end
A

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回答（2 个）

Amith Kamath
Amith Kamath 2011-11-21
for i = 1:7
for j = 1:7
P(i,j) = factorial(i + j - 2)./(2*factorial(j - 1));
end
end
for a 4x4 matrix, change the 7 in lines 1 and 2 to 4! But with this formulation, I wonder how it can be symmetric. I'm guessing you've mistyped the question and the denominator has to be (i-1)!(j-1)! which will set things correct!
http://en.wikipedia.org/wiki/Pascal_matrix
and hence the line 3 in the code above will be:
P(i,j) = factorial(i + j - 2)./(factorial(j - 1)*factorial(i - 1));
Oh, and BTW, MATLAB (as usual), has a function called pascal, and you need to just say pascal(4) or pascal(7)!
Andrei Bobrov
Andrei Bobrov 2011-11-21
n = 7;
k = factorial(0:n-1);
out = factorial(bsxfun(@plus,1:n,(1:n)')-2)./bsxfun(@times,k,k');

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